Pentagon chief Pete Hegseth said late on Friday his department was ending all military training, fellowships, and certificate programs with Harvard University in what marks the Trump administration's escalation against the Ivy League school.

"The @DeptWar is formally ending ALL Professional Military Education, fellowships, and certificate programs with Harvard University," Hegseth said in a statement on social media website X, labeling Harvard as "woke."

President Donald Trump's administration has cracked down on top US universities, including Harvard, over a range of issues such as pro-Palestinian protests against US ally Israel's assault on Gaza, diversity programs, transgender policies and climate initiatives.

Rights advocates have raised concerns about free speech, academic freedom and due process. Harvard did not immediately respond to a request for comment.

The university has previously sued the Trump administration over the government's attempt to freeze federal funding for the university.